Binghnetty Logistic Regression 3

R Software Module: rwasp_logisticregression.wasp (opens new window with default values)

Title produced by software: Bias-Reduced Logistic Regression

Date of computation: Wed, 30 Jan 2008 01:59:38 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/30/t12016836451ox49wz8atxiqti.htm/, Retrieved Wed, 30 Jan 2008 10:00:45 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1 1 5.3 2 1 1 4.6 2 1 1 5.9 2 1 1 6.4 2 1 1 4.5 2 1 1 3.1 2 1 1 3.8 2 1 1 5.7 2 1 1 3.6 2 1 1 3.6 2 1 1 6.1 2 1 1 5.3 2 1 1 4.3 2 1 1 6.5 2 1 1 6.2 2 1 1 6.9 2 1 1 7.2 2 1 1 6.6 2 1 1 5.7 2 1 1 6.8 2 1 1 2.2 2 1 1 2.2 2 1 1 4.1 2 1 1 5.2 2 1 1 5.8 2 1 1 5.2 2 1 1 5.6 2 1 1 5.7 2 1 1 4.4 2 1 1 5.4 2 1 1 6.1 2 1 1 6.5 2 1 1 4.7 2 1 1 6.8 2 1 1 6.3 2 1 1 3.8 2 1 1 3.1 2 1 1 6.5 2 1 1 7.1 2 1 1 1.0 2 1 0 4.9 2 1 0 5.8 2 1 0 5.6 2 1 0 4.9 2 1 0 5.2 2 1 0 7.0 2 0 1 5.0 2 0 1 8.0 2 0 0 6.0 2 0 1 5.0 2 0 1 8.0 2 0 0 10.0 2 0 1 1.0 2 0 1 7.0 2 0 1 6.0 2 0 1 4.0 2 0 0 6.0 2 0 0 6.0 2 0 1 8.0 2 0 0 7.0 2 0 0 6.0 2 0 1 7.0 2 0 1 6.0 2 0 1 6.0 2 0 0 6.0 2 0 1 5.0 2 0 1 6.0 2 0 1 7.0 2 0 1 6.0 2 0 1 3.0 2 0 1 6.0 2 0 1 3.0 2 0 1 7.0 2 0 1 5.0 2 0 1 7.0 2 0 1 5.0 2 0 1 7.0 2 0 1 7.0 2 0 1 6.0 2 0 1 7.0 2 0 1 5.0 2 0 1 6.0 2 0 1 6.0 2 0 1 6.0 2 0 1 5.0 2 0 1 8.0 2 0 0 3.0 2 0 0 5.0 2 0 0 6.0 2 0 0 6.0 2 0 1 6.0 2 0 0 99.0 2 0 1 8.0 2 0 1 8.0 2 0 0 4.0 2 0 1 9.0 2 0 1 5.0 2 0 0 6.0 2 0 1 99.0 2 0 1 6.0 2 0 1 6.0 2 0 1 7.0 2 0 1 5.0 2 0 0 99.0 2 0 1 6.0 2 0 1 6.0 2 0 0 6.0 2 0 1 7.0 2 0 0 8.0 2 0 0 7.0 2 0 1 6.0 2 0 2 6.0 2 0 1 5.0 2 0 1 7.0 2 0 1 6.0 2 0 0 7.0 2 0 1 9.0 2 0 1 6.0 2 0 1 7.0 2 0 1 6.0 2 0 1 7.0 2 0 1 7.0 2 0 0 8.0 2 0 1 4.0 2 0 0 5.0 2 0 1 6.0 2 0 1 6.0 2 0 1 6.0 2 0 1 7.0 2 1 1 7.8 1 1 1 6.0 1 1 1 6.0 1 1 1 7.1 1 1 1 5.9 1 1 1 3.6 1 1 1 6.9 1 1 1 8.0 1 1 1 5.6 1 1 1 6.1 1 1 1 5.1 1 1 1 5.0 1 1 1 5.2 1 1 1 2.9 1 1 1 4.9 1 1 1 4.7 1 1 1 6.5 1 1 1 7.5 1 1 1 3.9 1 1 1 3.2 1 1 1 4.5 1 1 1 6.5 1 1 1 7.4 1 1 1 3.3 1 1 1 5.9 1 1 1 4.8 1 1 1 4.4 1 1 1 5.4 1 1 1 5.9 1 1 1 6.1 1 1 1 5.4 1 1 1 6.0 1 1 1 4.9 1 1 1 5.3 1 1 1 6.0 1 1 1 3.2 1 1 1 6.5 1 1 1 3.6 1 1 1 5.9 1 1 1 5.2 1 1 1 7.3 1 1 1 8.9 1 1 1 1.8 1 1 1 6.5 1 1 1 3.0 1 1 1 7.0 1 1 1 7.0 1 1 1 5.9 1 1 1 6.3 1 1 1 3.8 1 1 1 7.6 1 1 1 6.3 1 1 1 5.6 1 1 1 6.4 1 1 1 7.5 1 1 1 7.0 1 1 1 1.1 1 1 1 6.0 1 1 1 6.5 1 1 1 5.7 1 1 1 5.5 1 1 1 6.4 1 1 1 6.5 1 1 1 1.9 1 1 1 3.4 1 1 1 6.4 1 1 1 1.6 1 1 1 6.8 1 1 1 6.1 1 1 1 6.3 1 1 0 5.1 1 1 0 4.7 1 1 0 4.1 1 1 0 3.0 1 1 0 6.5 1 1 0 5.3 1 1 0 6.4 1 1 0 6.8 1 0 1 12.0 1 0 1 7.0 1 0 0 6.0 1 0 1 5.0 1 0 1 7.0 1 0 1 8.0 1 0 0 5.0 1 0 1 8.0 1 0 1 5.0 1 0 1 6.0 1 0 1 9.0 1 0 0 7.0 1 0 1 6.0 1 0 0 6.0 1 0 0 7.0 1 0 0 6.0 1 0 0 6.0 1 0 0 8.0 1 0 0 7.0 1 0 0 5.0 1 0 0 7.0 1 0 0 7.0 1 0 1 6.0 1 0 1 5.0 1 0 1 7.0 1 0 0 8.0 1 0 1 8.0 1 0 0 9.0 1 0 0 99.0 1 0 0 8.0 1 0 0 6.0 1 0 1 5.0 1 0 1 9.0 1 0 1 7.0 1 0 1 6.0 1 0 1 7.0 1 0 0 6.0 1 0 0 6.0 1 0 1 7.0 1 0 1 7.0 1 0 0 6.0 1 0 1 6.0 1 0 0 6.0 1 0 0 8.0 1 0 1 6.0 1 0 0 7.0 1 0 1 7.0 1 0 1 5.0 1 0 0 8.0 1 0 1 4.0 1 0 1 7.0 1 0 1 8.0 1 0 1 10.0 1 0 1 6.0 1 0 0 7.0 1 0 1 5.0 1 0 0 6.0 1 0 0 6.0 1 0 0 10.0 1 0 0 7.0 1 0 0 6.0 1

Text written by user:

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Coefficients of Bias-Reduced Logistic Regression Variable Parameter S.E. t-stat 2-sided p-value (Intercept) 3.80668823578529 0.876644823590894 4.34233812069113 2.01116086806508e-05 snoring 1.39318066175670 0.351278268478411 3.96603145361475 9.4183394305336e-05 sleep_time -0.540332640756327 0.108879632513600 -4.96266040105192 1.24795605160877e-06 sex -1.22653768717192 0.291721501925025 -4.20448160001297 3.58609574284685e-05 Summary of Bias-Reduced Logistic Regression Deviance 299.232873990727 Penalized deviance 286.213583359798 Residual Degrees of Freedom 264 ROC Area 0.780129928315412 Hosmer–Lemeshow test Chi-square 17.7831143534614 Degrees of Freedom 8 P(>Chi) 0.0229126034525216 Fit of Logistic Regression Index Actual Fitted Error 1 1 0.470790927070424 0.529209072929576 2 1 0.564946832138264 0.435053167861736 3 1 0.391462441591778 0.608537558408222 4 1 0.329303837718878 0.670696162281122 5 1 0.578177581526662 0.421822418473338 6 1 0.744931919072306 0.255068080927694 7 1 0.666751618533598 0.333248381466402 8 1 0.417485922076200 0.5825140779238 9 1 0.69031578097212 0.309684219027879 10 1 0.69031578097212 0.309684219027879 11 1 0.366041777193257 0.633958222806743 12 1 0.470790927070424 0.529209072929576 13 1 0.604287745667261 0.395712254332739 14 1 0.317481812523903 0.682518187476097 15 1 0.353596189100147 0.646403810899853 16 1 0.272593915590655 0.727406084409345 17 1 0.241659736845527 0.758340263154473 18 1 0.305890633438332 0.694109366561668 19 1 0.417485922076200 0.5825140779238 20 1 0.283438596500826 0.716561403499174 21 1 0.826075045532568 0.173924954467432 22 1 0.826075045532568 0.173924954467432 23 1 0.629816504108966 0.370183495891034 24 1 0.484271139264305 0.515728860735695 25 1 0.404406989909573 0.595593010090427 26 1 0.484271139264305 0.515728860735695 27 1 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-0.781028149419593 240 0 0.291179468847894 -0.291179468847894 241 0 0.54760603873891 -0.54760603873891 242 0 0.675098240991562 -0.675098240991562 243 0 0.54760603873891 -0.54760603873891 244 0 0.34032521331786 -0.34032521331786 245 0 0.34032521331786 -0.34032521331786 246 0 0.54760603873891 -0.54760603873891 247 0 0.54760603873891 -0.54760603873891 248 0 0.34032521331786 -0.34032521331786 249 0 0.675098240991562 -0.675098240991562 250 0 0.34032521331786 -0.34032521331786 251 0 0.148994325224077 -0.148994325224077 252 0 0.675098240991562 -0.675098240991562 253 0 0.231088000282078 -0.231088000282078 254 0 0.54760603873891 -0.54760603873891 255 0 0.781028149419593 -0.781028149419593 256 0 0.148994325224077 -0.148994325224077 257 0 0.859603496793332 -0.859603496793332 258 0 0.54760603873891 -0.54760603873891 259 0 0.413544924210361 -0.413544924210361 260 0 0.193099432567248 -0.193099432567248 261 0 0.675098240991562 -0.675098240991562 262 0 0.231088000282078 -0.231088000282078 263 0 0.781028149419593 -0.781028149419593 264 0 0.34032521331786 -0.34032521331786 265 0 0.34032521331786 -0.34032521331786 266 0 0.0560845692686134 -0.0560845692686134 267 0 0.231088000282078 -0.231088000282078 268 0 0.34032521331786 -0.34032521331786 Type I & II errors for various threshold values Threshold Type I Type II 0.01 0 0.972222222222222 0.02 0 0.965277777777778 0.03 0 0.965277777777778 0.04 0 0.965277777777778 0.05 0 0.951388888888889 0.06 0 0.944444444444444 0.07 0 0.944444444444444 0.08 0 0.9375 0.09 0.00806451612903226 0.916666666666667 0.1 0.00806451612903226 0.909722222222222 0.11 0.00806451612903226 0.895833333333333 0.12 0.00806451612903226 0.895833333333333 0.13 0.00806451612903226 0.895833333333333 0.14 0.00806451612903226 0.833333333333333 0.15 0.0161290322580645 0.798611111111111 0.16 0.0241935483870968 0.798611111111111 0.17 0.0241935483870968 0.798611111111111 0.18 0.0241935483870968 0.756944444444444 0.19 0.032258064516129 0.756944444444444 0.2 0.032258064516129 0.75 0.21 0.032258064516129 0.736111111111111 0.22 0.0483870967741935 0.736111111111111 0.23 0.0483870967741935 0.736111111111111 0.24 0.0483870967741935 0.680555555555556 0.25 0.0564516129032258 0.680555555555556 0.26 0.0725806451612903 0.680555555555556 0.27 0.0725806451612903 0.576388888888889 0.28 0.0806451612903226 0.576388888888889 0.29 0.104838709677419 0.576388888888889 0.3 0.112903225806452 0.5625 0.31 0.129032258064516 0.555555555555556 0.32 0.153225806451613 0.555555555555556 0.33 0.161290322580645 0.555555555555556 0.34 0.161290322580645 0.555555555555556 0.35 0.169354838709677 0.472222222222222 0.36 0.177419354838710 0.472222222222222 0.37 0.193548387096774 0.472222222222222 0.38 0.193548387096774 0.319444444444444 0.39 0.193548387096774 0.319444444444444 0.4 0.201612903225806 0.319444444444444 0.41 0.209677419354839 0.319444444444444 0.42 0.241935483870968 0.291666666666667 0.43 0.25 0.291666666666667 0.44 0.266129032258065 0.284722222222222 0.45 0.266129032258065 0.284722222222222 0.46 0.282258064516129 0.284722222222222 0.47 0.290322580645161 0.270833333333333 0.48 0.306451612903226 0.270833333333333 0.49 0.338709677419355 0.270833333333333 0.5 0.346774193548387 0.270833333333333 0.51 0.354838709677419 0.270833333333333 0.52 0.362903225806452 0.201388888888889 0.53 0.362903225806452 0.201388888888889 0.54 0.370967741935484 0.201388888888889 0.55 0.395161290322581 0.138888888888889 0.56 0.403225806451613 0.138888888888889 0.57 0.419354838709677 0.138888888888889 0.58 0.435483870967742 0.138888888888889 0.59 0.435483870967742 0.138888888888889 0.6 0.451612903225806 0.138888888888889 0.61 0.459677419354839 0.138888888888889 0.62 0.508064516129032 0.138888888888889 0.63 0.540322580645161 0.138888888888889 0.64 0.564516129032258 0.138888888888889 0.65 0.564516129032258 0.125 0.66 0.564516129032258 0.125 0.67 0.604838709677419 0.125 0.68 0.64516129032258 0.0763888888888889 0.69 0.685483870967742 0.0763888888888889 0.7 0.701612903225806 0.0763888888888889 0.71 0.709677419354839 0.0763888888888889 0.72 0.709677419354839 0.0694444444444444 0.73 0.733870967741935 0.0694444444444444 0.74 0.741935483870968 0.0694444444444444 0.75 0.774193548387097 0.0694444444444444 0.76 0.782258064516129 0.0555555555555556 0.77 0.798387096774194 0.0555555555555556 0.78 0.806451612903226 0.0555555555555556 0.79 0.814516129032258 0.0138888888888889 0.8 0.838709677419355 0.0138888888888889 0.81 0.846774193548387 0.0138888888888889 0.82 0.846774193548387 0.0138888888888889 0.83 0.870967741935484 0.0138888888888889 0.84 0.879032258064516 0.0138888888888889 0.85 0.879032258064516 0.0138888888888889 0.86 0.879032258064516 0.00694444444444444 0.87 0.887096774193548 0.00694444444444444 0.88 0.89516129032258 0.00694444444444444 0.89 0.911290322580645 0.00694444444444444 0.9 0.92741935483871 0.00694444444444444 0.91 0.951612903225806 0 0.92 0.967741935483871 0 0.93 0.967741935483871 0 0.94 0.967741935483871 0 0.95 0.967741935483871 0 0.96 0.991935483870968 0 0.97 1 0 0.98 1 0 0.99 1 0

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t12016836451ox49wz8atxiqti/158ww1201683568.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t12016836451ox49wz8atxiqti/158ww1201683568.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t12016836451ox49wz8atxiqti/28l6n1201683568.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t12016836451ox49wz8atxiqti/28l6n1201683568.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

library(brlr) roc.plot <- function (sd, sdc, newplot = TRUE, ...) { sall <- sort(c(sd, sdc)) sens <- 0 specc <- 0 for (i in length(sall):1) { sens <- c(sens, mean(sd >= sall[i], na.rm = T)) specc <- c(specc, mean(sdc >= sall[i], na.rm = T)) } if (newplot) { plot(specc, sens, xlim = c(0, 1), ylim = c(0, 1), type = 'l', xlab = '1-specificity', ylab = 'sensitivity', main = 'ROC plot', ...) abline(0, 1) } else lines(specc, sens, ...) npoints <- length(sens) area <- sum(0.5 * (sens[-1] + sens[-npoints]) * (specc[-1] - specc[-npoints])) lift <- (sens - specc)[-1] cutoff <- sall[lift == max(lift)][1] sensopt <- sens[-1][lift == max(lift)][1] specopt <- 1 - specc[-1][lift == max(lift)][1] list(area = area, cutoff = cutoff, sensopt = sensopt, specopt = specopt) } roc.analysis <- function (object, newdata = NULL, newplot = TRUE, ...) { if (is.null(newdata)) { sd <- object$fitted[object$y == 1] sdc <- object$fitted[object$y == 0] } else { sd <- predict(object, newdata, type = 'response')[newdata$y == 1] sdc <- predict(object, newdata, type = 'response')[newdata$y == 0] } roc.plot(sd, sdc, newplot, ...) } hosmerlem <- function (y, yhat, g = 10) { cutyhat <- cut(yhat, breaks = quantile(yhat, probs = seq(0, 1, 1/g)), include.lowest = T) obs <- xtabs(cbind(1 - y, y) ~ cutyhat) expect <- xtabs(cbind(1 - yhat, yhat) ~ cutyhat) chisq <- sum((obs - expect)^2/expect) P <- 1 - pchisq(chisq, g - 2) c('X^2' = chisq, Df = g - 2, 'P(>Chi)' = P) } x <- as.data.frame(t(y)) r <- brlr(x) summary(r) rc <- summary(r)$coeff hm <- hosmerlem(y[1,],r$fitted.values) hm bitmap(file='test0.png') ra <- roc.analysis(r) dev.off() te <- array(0,dim=c(2,99)) for (i in 1:99) { threshold <- i / 100 numcorr1 <- 0 numfaul1 <- 0 numcorr0 <- 0 numfaul0 <- 0 for (j in 1:length(r$fitted.values)) { if (y[1,j] > 0.99) { if (r$fitted.values[j] >= threshold) numcorr1 = numcorr1 + 1 else numfaul1 = numfaul1 + 1 } else { if (r$fitted.values[j] < threshold) numcorr0 = numcorr0 + 1 else numfaul0 = numfaul0 + 1 } } te[1,i] <- numfaul1 / (numfaul1 + numcorr1) te[2,i] <- numfaul0 / (numfaul0 + numcorr0) } bitmap(file='test1.png') op <- par(mfrow=c(2,2)) plot((1:99)/100,te[1,],xlab='Threshold',ylab='Type I error', main='1 - Specificity') plot((1:99)/100,te[2,],xlab='Threshold',ylab='Type II error', main='1 - Sensitivity') plot(te[1,],te[2,],xlab='Type I error',ylab='Type II error', main='(1-Sens.) vs (1-Spec.)') plot((1:99)/100,te[1,]+te[2,],xlab='Threshold',ylab='Sum of Type I & II error', main='(1-Sens.) + (1-Spec.)') par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Coefficients of Bias-Reduced Logistic Regression',5,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'t-stat',header=TRUE) a<-table.element(a,'2-sided p-value',header=TRUE) a<-table.row.end(a) for (i in 1:length(rc[,1])) { a<-table.row.start(a) a<-table.element(a,labels(rc)[[1]][i],header=TRUE) a<-table.element(a,rc[i,1]) a<-table.element(a,rc[i,2]) a<-table.element(a,rc[i,3]) a<-table.element(a,2*(1-pt(abs(rc[i,3]),r$df.residual))) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Summary of Bias-Reduced Logistic Regression',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Deviance',1,TRUE) a<-table.element(a,r$deviance) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Penalized deviance',1,TRUE) a<-table.element(a,r$penalized.deviance) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Residual Degrees of Freedom',1,TRUE) a<-table.element(a,r$df.residual) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'ROC Area',1,TRUE) a<-table.element(a,ra$area) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Hosmer–Lemeshow test',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Chi-square',1,TRUE) a<-table.element(a,hm[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Degrees of Freedom',1,TRUE) a<-table.element(a,hm[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'P(>Chi)',1,TRUE) a<-table.element(a,hm[3]) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Fit of Logistic Regression',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Index',1,TRUE) a<-table.element(a,'Actual',1,TRUE) a<-table.element(a,'Fitted',1,TRUE) a<-table.element(a,'Error',1,TRUE) a<-table.row.end(a) for (i in 1:length(r$fitted.values)) { a<-table.row.start(a) a<-table.element(a,i,1,TRUE) a<-table.element(a,y[1,i]) a<-table.element(a,r$fitted.values[i]) a<-table.element(a,y[1,i]-r$fitted.values[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Type I & II errors for various threshold values',3,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Threshold',1,TRUE) a<-table.element(a,'Type I',1,TRUE) a<-table.element(a,'Type II',1,TRUE) a<-table.row.end(a) for (i in 1:99) { a<-table.row.start(a) a<-table.element(a,i/100,1,TRUE) a<-table.element(a,te[1,i]) a<-table.element(a,te[2,i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable3.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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